Question

How do you solve `x+2y=2` and `2x+4y=4`?

Answer 1

This sistem is indeterminate because the second equation is the first multiplied by `2`.

Answer 2

`x+2y=2` and `2x+4y=4`

Whether you try to solve by substitution or by addition/subtraction, you will eventually get `0=0`

This tells us that any solution to one equation is also a solution to the other. (The equations are equivalent.) There are other ways to see the same thing:
One equation is simply a multiple of the other.
Though of as equations on lines, the lines coincide.
In slope intercept form, both lines are: `y=-1/2 x+1`.

The solutions to the system are exactly the solutions of the equation. (In a sense, there is really only one equation.)

The solution set can be written in various ways. Here are some of them:

`"All " (x,y) " with " x+2y=2`

`"All " (x, 1-1/2x)`

`"All " (-2y+2, x)`